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Mathematics-Online course: Vector Calculus - Planes

Distance Point - Plane

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Given a plane with normal vector $ \vec{n}$ through point $ P$ . Let $ X$ be the perpendicular projection of a given point $ Q$ onto this plane. The so called perpendicular vector of point $ Q$ onto the plane is given by

$\displaystyle \overrightarrow{XQ} = \frac{\overrightarrow{PQ}\cdot\vec{n}} {\vert\vec{n}\vert^2}\,\vec{n}\,. $

Its length

$\displaystyle d = \frac{\vert\overrightarrow{PQ}\cdot\vec{n}\vert} {\vert\vec{n}\vert} $

is the distance of the plane from $ Q$ .
\includegraphics[width=10cm]{abstand}

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  automatically generated 10/30/2007